Photodetachment cross-section evaluation using asymptotic considerations

Mathematical calculations are given concerning the evaluation of the negative ions photodetachment cross-section , into a so-called saturation regime. The interaction between a negative ion particle beam and a laser beam is examined under theoretical aspects. A quantitative criterion S is proposed to define the saturation threshold between the linear and the saturated domains, which are both present in this saturation regime. The asymptotic behaviours extracted at the low and high energy limits are used to determine this threshold quantitative criterion S and to evaluate also the photodetachment cross-section . The case of a symmetric gaussian photodetachment laser beam shape is examined according to the proposed formalism, which can be used either for the photo-detachment or photo-ionization processes, and could be potentially used into technological solutions for negative ion neutralisation processes (such as neutral beam injector) in the future fusion energy devices. Estimations onto the errors related to the use of this methodology are given.